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Centralizer and normalizer

In mathematics, especially group theory, the centralizer (also called commutant) of a subsetS in a groupG is the set CG⁡(S){\displaystyle \operatorname {C} _{G}(S)} of elements of G that commute with every element of S, or equivalently, the set of elements g∈G{\displaystyle g\in G} such that conjugation by g{\displaystyle g} leaves each element of S fixed.

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